A NOTE ON LATTICE OPERATIONS OF RIESZ SPACES OF ORDER BOUNDED OPERATORS

Authors

  • BORIS LAVRIČ Institute of Mathematics, Physics and Mechanics, Jadranska 19, 61000 Ljubljana, Yugoslavuia.

DOI:

https://doi.org/10.5556/j.tkjm.21.1990.4688

Keywords:

Riesz space, order bounded linear operator, lattice operation, Freudenthal's spectral theorem.

Abstract

Let $L$, $M$ be Archimedean Riesz spaces with $M$ Dedekind complete, and let $\mathcal L_b(L,M )$ be the Riesz space of order bounded linear operators from $L$ into $M$. A theorem of Abramovic [1] on lattice operations of $\mathcal L_b(L,M )$ is generalized on Riesz spaces $L$ in which a weak form of Freudenthal's spectral theorem [4] holds.

References

J. A. Abramovic, "Injective envelopes of normed lattices," Soviet Math. Dokl. 12 (1971), 511-514.

C. D. Aliprantis and O. Burkinshaw, "The components of a positive operator," Math. Z. 184 (1983), 245-257.

C. D. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, New York (1985).

B. Lavric, "On Freudentthal's spectral theorem," Proc. Kon. Ned. Akad. Wetensch 89 (1986), 411-421.

W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam (1971).

W. A. J. Luxemburg and A. C. Zaanen, "The linear modulus of an order bounded linear transformation I," Proc. Kon. Ned. Akad. Wetensch 74 (1971), 422-434.

A. I. Veksler, "Projection properties of vector lattices and Freudenthal's spectral theorem," (Russian) Math. Nachr. 74 (1976), 7-25.

A. C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam (1983).

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Published

1990-12-01

How to Cite

LAVRIČ, B. (1990). A NOTE ON LATTICE OPERATIONS OF RIESZ SPACES OF ORDER BOUNDED OPERATORS. Tamkang Journal of Mathematics, 21(4), 395–398. https://doi.org/10.5556/j.tkjm.21.1990.4688

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Papers